Noam Hazon

Redundancy, Efficiency and Robustness in Multi-Robot Coverage

Area coverage is an important task for mobile robots, with many real-world applications. Motivated by potential efficiency and robustness improvements, there is growing interest in the use of multiple robots in coverage. Previous investigations of multi-robot coverage focuses on completeness and eliminating redundancy, but does not formally address robustness, nor examine the impact of the initial positions of robots on the coverage time. Indeed, a common assumption is that non-redundancy leads to improved coverage time. We address robustness and efficiency in a family of multi-robot coverage algorithms, based on spanning-tree coverage of approximate cell decomposition. We analytically show that the algorithms are robust, in that as long as a single robot is able to move, the coverage will be completed. We also show that non-redundant (non-back tracking) versions of the algorithms have a worst-case coverage time virtually identical to that of a single robot—thus no performance gain is guaranteed in non-redundant coverage. Moreover, this worst-case is in fact common in real-world applications. Surprisingly, however, redundant coverage algorithms lead to guaranteed performance which halves the coverage time even in the worst case.

On redundancy, efficiency, and robustness in coverage for multiple robots

Motivated by potential efficiency and robustness gains, there is growing interest in the use of multiple robots for coverage. In coverage, robots visit every point in a target area, at least once. Previous investigations of multi-robot coverage focus on completeness of the coverage, and on eliminating redundancy, but do not formally address robustness. Moreover, a common assumption is that elimination of redundancy leads to improved efficiency (coverage time). We address robustness and efficiency in a novel family of multi-robot coverage algorithms, based on spanning-tree coverage of approximate cell decomposition of the work-area. We analytically show that the algorithms are robust, in that as long as a single robot is able to move, the coverage will be completed. We also show that non-redundant (non-backtracking) versions of the algorithms have a worst-case coverage time virtually identical to that of a single robot-thus no performance gain is guaranteed in non-redundant coverage. Surprisingly, however, redundant coverage algorithms lead to guaranteed performance which halves the coverage time even in the worst case. We present a polynomial-time redundant coverage algorithm, whose coverage time is optimal, and which is able to address robots heterogeneous in speed and fuel. We compare the performance of all algorithms empirically and show that the use of the optimal algorithm leads to significant improvements in coverage time.

Constructing spanning trees for efficient multi-robot coverage

This paper discusses the problem of building efficient coverage paths for a team of robots. An efficient multirobot coverage algorithm should result in a coverage path for every robot, such that the union of all paths generates a full coverage of the terrain and the total coverage time is minimized. A method, underlying several coverage algorithms, suggests the use of spanning trees as base for creating coverage paths. Current studies assume that the spanning tree is given, and try to make the most out of the given configuration. However, overall performance of the coverage is heavily dependent on the given spanning tree. This paper tackles the open challenge of constructing a coverage spanning tree that minimizes the time to complete coverage. We argue that the choice of the initial spanning tree has far reaching consequences concerning the coverage time, and if the tree is constructed appropriately, it could considerably reduce the coverage time of the terrain. Therefore the problem studied here is finding spanning trees that would decrease the coverage time of the terrain when used as base for multi-robot coverage algorithms. The main contributions of this paper are twofold. First, it provides initial sound discussion and results concerning the construction of the tree as a crucial base for any efficient coverage algorithm. Second, it describes a polynomial-time tree construction algorithm that, as shown in extensive simulations, dramatically improves the coverage time even when used as a basis for a simple, inefficient, coverage algorithm

Towards robust on-line multi-robot coverage

Area coverage is an important task for mobile robots, with many real-world applications. In many cases, the coverage has to be completed without the use of a map or any a priori knowledge about the area, a process referred-to as on-line coverage. Previous investigations of multi-robot on-line coverage focused on the improved efficiency gained from the use of multiple robots, but did not formally addressed the potential for greater robustness. We present a novel multi-robot on-line coverage algorithm, based on approximate cell decomposition. We analytically show that the algorithm is complete and robust, in that as long as a single robot is able to move, the coverage would be completed. We analyze the assumptions underlying the algorithm requirements and present a number of techniques for executing it in real robots. We show empirical coverage-time results of running the algorithm in two different environments and several group sizes

The giving tree: constructing trees for efficient offline and online multi-robot coverage

This paper discusses the problem of building efficient coverage paths for a team of robots. An efficient multi-robot coverage algorithm should result in a coverage path for every robot, such that the union of all paths generates a full coverage of the terrain and the total coverage time is minimized. A method underlying several coverage algorithms, suggests the use of spanning trees as base for creating coverage paths. However, overall performance of the coverage is heavily dependent on the given spanning tree. This paper focuses on the challenge of constructing a coverage spanning tree for both online and offline coverage that minimizes the time to complete coverage. Our general approach involves building a spanning tree by growing sub-trees from the initial location of the robots. This paper first describes a polynomial time tree-construction algorithm for offline coverage. The use of this algorithm is shown by extensive simulations to significantly improve the coverage time of the terrain even when used as a basis for a simple, inefficient, coverage algorithm. Second, this paper provides an algorithm for online coverage of a finite terrain based on spanning-trees, that is complete and guarantees linear time coverage with no redundancy in the coverage. In addition, the solutions proposed by this paper guarantee robustness to failing robots: the offline trees are used as base for robust multi-robot coverage algorithms, and the online algorithm is proven to be robust.

Enhancing comparison shopping agents through ordering and gradual information disclosure

The plethora of comparison shopping agents (CSAs) in today’s markets enables buyers to query more than a single CSA when shopping, thus expanding the list of sellers whose prices they obtain. This potentially decreases the chance of a purchase within any single interaction between a buyer and a CSA, and consequently decreases each CSAs’ expected revenue per-query. Obviously, a CSA can improve its competence in such settings by acquiring more sellers’ prices, potentially resulting in a more attractive “best price”. In this paper we suggest a complementary approach that improves the attractiveness of the best result returned based on intelligently controlling the order according to which they are presented to the user, in a way that utilizes several known cognitive-biases of human buyers. The advantage of this approach is in its ability to affect the buyer’s tendency to terminate her search for a better price, hence avoid querying further CSAs, without spending valuable resources on finding additional prices to present. The effectiveness of our method is demonstrated using real data, collected from four CSAs for five products. Our experiments confirm that the suggested method effectively influence people in a way that is highly advantageous to the CSA compared to the common method for presenting the prices. Furthermore, we experimentally show that all of the components of our method are essential to its success.

Negotiation Strategies for Agents with Ordinal Preferences

Negotiation is a very common interaction between automated agents. Many common negotiation protocols work with cardinal utilities, even though ordinal preferences, which only rank the outcomes, are easier to elicit from humans. In this work we concentrate on negotiation with ordinal preferences over a finite set of outcomes. We study an intuitive protocol for bilateral negotiation, where the two parties make offers alternately. We analyze the negotiation protocol under different settings. First, we assume that each party has full information about the other partys preference order. We provide elegant strategies that specify a sub-game perfect equilibrium for the agents. We further show how the studied negotiation protocol almost completely implements a known bargaining rule. Finally, we analyze the no information setting. We study several solution concepts that are distribution-free, and analyze both the case where neither party knows the preference order of the other party, and the case where only one party is uninformed.

Forming k coalitions and facilitating relationships in social networks

Abstract In this paper we relax two common assumptions that are made when studying coalition formation. The first is that any number of coalitions can be formed; the second is that any possible coalition can be formed. We study a model of coalition formation where the value depends on a social network and exactly k coalitions must be formed. Additionally, in this context we present a new problem for an organizer that would like to introduce members of the social network to each other in order to increase the social welfare or to stabilize a coalition structure. We show that, when the number of coalitions, k, is fixed and there are not many negative edges, it is possible to find the coalition structure that maximizes the social welfare in polynomial time. Furthermore, an organizer can efficiently find the optimal set of edges to add to the network, and we experimentally demonstrate the effectiveness of this approach. In addition, we show that in our setting even when k is fixed and there are not many negative edges, finding a member of the core is intractable. However, we provide a heuristic for efficiently finding a member of the core that also guarantees a social welfare within a factor of 1/2 of the optimal social welfare. We also show that checking whether a given coalition structure is a member of the core can be done in polynomial time. Finally, we consider the problem faced by an organizer who would like to add edges to the network in order to stabilize a specific coalition structure core: we show that this problem is intractable.

Optimal defense against election control by deleting voter groups

Abstract Election control encompasses attempts from an external agent to alter the structure of an election in order to change its outcome. This problem is both a fundamental theoretical problem in social choice, and a major practical concern for democratic institutions. Consequently, this issue has received considerable attention, particularly as it pertains to different voting rules. In contrast, the problem of how election control can be prevented or deterred has been largely ignored. We introduce the problem of optimal defense against election control, including destructive and constructive control, where manipulation is allowed at the granularity of groups of voters (e.g., voting locations) through a denial-of-service attack, and the defender allocates limited protection resources to prevent control. We consider plurality voting, and show that it is computationally hard to prevent both types of control, though destructive control itself can be performed in polynomial time. For defense against destructive control, we present a double-oracle framework for computing an optimal prevention strategy. We show that both defender and attacker best response subproblems are NP-complete, and develop exact mixed-integer linear programming approaches for solving these, as well as fast heuristic methods. We then extend this general approach to develop effective algorithmic solutions for defense against constructive control. Finally, we generalize the model and algorithmic approaches to consider uncertainty about voter preferences. Experiments conducted on both synthetic and real data demonstrate that the proposed computational framework can scale to realistic problem instances. 1